The Capital Asset Pricing Model
Now we know how people should invest, if they dislike variance and like E(R) Now we ask, given this behavior, can we say anything? We are particularly interested in this question: : Why do some assets have high E(R)s (low prices) and some assets have low E(R)s (high prices)?
What should the ER of an asset be?
Logical: the more investors hate an asset, the its price should be, and the its ER should be Two stocks, both expected to pay $100 next period (and then die), both have a
What's the current price/ER of each? What should happen to the price/ER of each? What would make investors dislike an asset? One possibility: risk
Variances as a measure of risk
Probability
Payoff on 1 share of XOM
Payoff on one share of GRMN
0.2ff
120
112
0.ff
110
110
0.2ff
100
108
How much do you make on average in each? (What's your "expected payoff"?)
Suppose everyone was willing to pay $100 (and no more) for one share of XOM. :What is the expected return on XOM? How much should everyone be willing to pay for one share of GRMN? What should the expected return on GRMN be?
If assets are fairly priced, assets with high risk will have expected returns Why? Everyone hates them. So they won't want to buy them unless their prices are (i.e., their expected returns are ).
: Is A overpriced/underpriced?
If assets are fairly priced, assets with high expected returns are those which have risk
What
Given their risk, how much every asset should be paying High risk assets should have. expected returns
Problem
Variance ("spreadoutness") is not enough to measure risk When you combine assets into portfolios, some of the risk vanishes. Why? Cancelling out, "diversification"
Example
I write on a price of paper: I will toss a coin, and give the bearer $160 if it comes up heads and $60 if it comes up tails Does this paper have risk (variance)? How much are you willing to pay me for this piece of paper? Are you willing to pay me $110? Suppose you're only willing to pay me $100. Suppose everyone is like you. How much can I sell this paper for? What is the fair value of this piece of paper? What is the expected return on this piece of paper? Suppose I try to sell another piece of paper, but this time... Same questions
Suppose person X buys both pieces of paper :What is the payoff on her portfolio? :What is the expected payoff? Does her portfolio have risk? Why not? : Cancelling out: "diversification" How much would X be willing to pay me for both pieces of paper? For each? X exists in the marketplace. How much would the pieces of paper sell for to anyone else? What is the expected return on the pieces of paper if they're fairly pr